1.

Prove that the infinitesimals alpha=x and beta=x cos (1//x) (as x to 0) are not comparable, ie, their ratio has no limit.

Answer»


ANSWER :(a) 100x is an INFINITESIMAL of the same order as X; (b) `x^(2)` is an infinitesimal of an order higher than x; (c) 6 sin x is an infinitesimal of the same order as x; (d) `sin^(3)`x is an infinitesimal of an order higher than x.
(e) `ROOT3(TAN^(2)x)`


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